Class 10 Polynomials Quiz and Flashcards: बहुपद परिभाषा

Study Notes

Polynomials in Class 10 Maths

Polynomials are algebraic expressions that consist of variables and constants that are combined using only addition, subtraction, and multiplication. They play a crucial role in various mathematical fields, including algebra, calculus, and geometry. In Class 10 Maths, the concept of polynomials is introduced as part of the Algebra unit.

Introduction to Polynomials

A polynomial is an expression of the form a_n x^n + a_(n-1) x^(n-1) + ... + a_2 x^2 + a_1 x + a_0, where a_n, a_(n-1), ..., a_2, a_1, a_0 are constants and x is a variable. The highest power of x in the polynomial is called the degree of the polynomial.

Zeros of a Polynomial

The zeros of a polynomial are the values of x that make the polynomial equal to zero. For example, if p(x) = x^2 - 1, the zeros of p(x) are 1 and -1.

Relationship between Zeroes and Coefficients of a Polynomial

The relationship between the zeros and coefficients of a polynomial is given by the Factor Theorem, which states that if a is a zero of a polynomial p(x), then (x-a) is a factor of p(x).

Division Algorithm for Polynomials

The division algorithm for polynomials is similar to the division algorithm for integers. Given a polynomial p(x) and a non-zero polynomial q(x), there exist unique polynomials q(x), r(x), and q(x), such that p(x) = q(x) * q(x) + r(x), where the degree of r(x) is less than the degree of q(x).

Summary

Polynomials are essential in Class 10 Maths, as they form the basis for understanding more advanced mathematical concepts. Understanding the basics of polynomials, including their zeros, relationship between coefficients, and the division algorithm, is crucial for success in higher maths classes.

Description

Test your understanding of polynomials in Class 10 Maths, including their definition, zeros, relationship between coefficients, and division algorithm. This quiz covers the basics of polynomials and their importance in algebra and higher maths classes.